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# MCQ (Previous Year Questions) - Circles (Level 1)

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MCQ (Previous Year Questions) - Circles (Level 1) - Question 1

### The square of the length of tangent from (3, –4) on the circle x2 + y2 – 4x – 6y + 3 = 0     [AIEEE-2002]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 2

### If the two circles (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then [AIEEE-2003]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 3

### The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is               [AIEEE-2003]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 4

If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre is -

[AIEEE-2004]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 5

A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is -

[AIEEE-2004]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 6

If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10p, then the equation of the circle is -

[AIEEE-2004]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 7

If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct point P and Q then the lines 5x + by – a = 0 passes through P and Q for -

[AIEEE-2005]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 8

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is -

[AIEEE-2005]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 9

If a circle passes through the point (a, b) and cuts the circle x2 + y2 = porthogonally, then the equation of the locus of its centre is -

[AIEEE-2005]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 10

If the pair of line ax2 + 2(a + b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

[AIEEE-2005]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 11

If thel ines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49p square units, the equation of the circle is -

[AIEEE-2006]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 12

Let C be the circle with centre (0,0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle c that subtend an angle of at its centre is -

[AIEEE-2006]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 13

Consider a family of circles which are passing through the point (–1, 1) and are tangent to x-axis. If (h,k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

[AIEEE-2007]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 14

The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is -

MCQ (Previous Year Questions) - Circles (Level 1) - Question 15

The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

[AIEEE-2010]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 16

The two circles x2 + y2 = ax and x2 + y2 = c2 (c > 0) touch each other if :

[AIEEE-2011]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 17

The length of the diameter of the circle which touches the x-axis at the pint (1, 0) and passes through the point (2, 3)

[AIEEE-2012]

MCQ (Previous Year Questions) - Circles (Level 1) - Question 18

The circle passing through (1, –2) and touching the axis of x at (3, 0) also passes through the point :

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